The Airy process is a real valued random process whose finite dimensional distribution is determined by a Fredholm determinant with Airy kernel. It was first introduced by Prahofer and Spohn in the study of polynuclear growth model more than 20 years ago and has become a central object in the KPZ universality class. There has been some intensive research activities around the Airy process, some of which has rigourously proved its existence, time correlation and continuity, and more interestingly obtained the modulus of continuity. Compared to well-studied Brownian motions, Brownian bridges and even Ornstein-Ulenbeck processes, Airy process and its extension (i.e. Airy line ensembles) are new, so it is worthwhile further research. In this talk we shall briefly review some remarkable results in this field, no detailed proofs are given.

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